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Assembly Modes of General Planar 3-RPR Parallel Mechanisms when Using the Linear Actuators’ Orientations

  • Stefan SchulzEmail author
  • Arthur Seibel
  • Josef Schlattmann
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

In this paper, we show that the number of possible assembly modes for the general planar 3-RPR parallel mechanism, where P denotes active prismatic joints and R denotes passive revolute joints, can be significantly reduced when using the linear actuators’ orientations in-stead of their lengths. The linear actuators’ lengths lead to a univariate polynomial which can have up to six different solutions and thus provides up to six assembly modes. By measuring the orientations of the linear actuators, provided, e. g., by inertial measurement units, only two assembly modes exist. Furthermore, by using two orientations of the linear actuators in addition to the moveable manipulator platform’s orientation, only one assembly mode remains.

Keywords

assembly modes direct kinematics problem parallel kinematics 3-RPR parallel mechanism linear actuators’ orientations 

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References

  1. 1.
    Collins, C.L.: Forward kinematics of planar parallel manipulators in the Clifford algebra of P2. Mechanism and Machine Theory 37(8), 799–813 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Gosselin, C.M., Sefrioui, J., Richard, M.J.: Solutions polynomiales au problème de la cinématique directe des manipulateurs parallèles plans à trois degrés de liberté. Mechanism and Machine Theory 27(2), 107–119 (1992)CrossRefGoogle Scholar
  3. 3.
    Merlet, J.P.: Parallel Robots. Springer-Verlag, Dordrecht, The Netherlands (2006)Google Scholar
  4. 4.
    Peisach, E.E.: Determination of the position of the member of three-joint and two-joint four member assur groups with rotational pairs. Machinowedenie 5, 55–61 (1985). In RussianGoogle Scholar
  5. 5.
    Pennock, G.R., Kassner, D.J.: Kinematic analysis of a planar eight-bar linkage: Application to a platform-type robot. Journal of Mechanical Design 114(1), 87–95 (1992)CrossRefGoogle Scholar
  6. 6.
    Rojas, N., Thomas, F.: The forward kinematics of 3-RPR planar robots: A review and a distance-based formulation. IEEE Transactions on Robotics 27(1), 143–150 (2011)CrossRefGoogle Scholar
  7. 7.
    Schulz, S., Seibel, A., Schlattmann, J.: Closed-form solution for the direct kinematics problem of planar 3-RPR parallel mechanisms. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 968–973. Brisbane, Australia (2018)Google Scholar
  8. 8.
    Wohlhart, K.: Direct kinematic solution of the general planar Stewart platform. In: International Conference on Computer Integrated Manufacturing, pp. 403–411. Zakopane, Poland (1992)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Stefan Schulz
    • 1
    Email author
  • Arthur Seibel
    • 1
  • Josef Schlattmann
    • 1
  1. 1.Workgroup on System Technologies and Engineering Design MethodologyHamburg University of TechnologyHamburgGermany

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